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  FDR-control in multiscale change-point segmentation.

Li, H., Munk, A., & Sieling, H. (2016). FDR-control in multiscale change-point segmentation. Electronic Journal of Statistics, 10(1), 918-959. doi:10.1214/16-EJS1131.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002C-310B-5 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002C-DE50-5
Genre: Journal Article

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 Creators:
Li, H.1, Author              
Munk, A.1, Author              
Sieling, H., Author
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1Research Group of Statistical Inverse-Problems in Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_1113580              

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Free keywords: Multiscale inference; change-point regression; false discovery rate; deviation bound; dynamic programming; minimax lower bound; honest inference; array CGH data; ion channel recordings
 Abstract: Fast multiple change-point segmentation methods, which additionally provide faithful statistical statements on the number, locations and sizes of the segments, have recently received great attention. In this paper, we propose a multiscale segmentation method, FDRSeg, which controls the false discovery rate (FDR) in the sense that the number of false jumps is bounded linearly by the number of true jumps. In this way, it adapts the detection power to the number of true jumps. We prove a non-asymptotic upper bound for its FDR in a Gaussian setting, which allows to calibrate the only parameter of FDRSeg properly. Moreover, we show that FDRSeg estimates change-point locations, as well as the signal, in a uniform sense at optimal minimax convergence rates up to a log-factor. The latter is w.r.t. Lp-risk, p≥1, over classes of step functions with bounded jump sizes and either bounded, or even increasing, number of change-points. FDRSeg can be efficiently computed by an accelerated dynamic program; its computational complexity is shown to be linear in the number of observations when there are many change-points. The performance of the proposed method is examined by comparisons with some state of the art methods on both simulated and real datasets. An R-package is available online.

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Language(s): eng - English
 Dates: 2016
 Publication Status: Published online
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 Rev. Method: Peer
 Identifiers: DOI: 10.1214/16-EJS1131
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Title: Electronic Journal of Statistics
Source Genre: Journal
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Pages: - Volume / Issue: 10 (1) Sequence Number: - Start / End Page: 918 - 959 Identifier: -